| Combinatorics (1): counting principles and methods
| Combinatorics (2): Counting problems using recurrence relations. Recurrences and generating functions.
| Discrete probabilities (1): Axiomatic definition of probability. General formulas and properties. Interpretation of probabilities. Examples.
| Discrete probabilities (2): Conditional probabilities. Formula on total probability and Bayes formula.
| Discrete probabilities (3): Classical probability schemes. Discrete random variables.
| Discrete probabilities (4): Expected value, variance. Examples of discrete random variables with their expected value and variance.
| Discrete probabilities (5): Weak law of large numbers. Markov theorem, Chebyshev theorem, Poisson theorem. Examples and applications.
| Graph theory (1): Directed and undirected graphs, multigraphs: definitions, notations, general properties. Examples of problems which can be modelled with graphs. Euler’s theorem.
| Graph theory (2): Walks, trails, paths, cycles. Connectivity in graphs. Isomorphic graphs. Subgraphs. Examples of graphs. Operations with graphs. Trees: general properties.
| Graph theory (3): Trees, directed trees, rooted trees, spanning trees, minimum spanning trees (MST) in weighted graphs. Algorithms for MST: Prim, Kruskal, Edmonds – Chu-Liu.
| Graph theory (4): DFS (depth-first-search) and BFS (breadth-first- search) trees. Properties of BFS trees. Minimum path, Dijkstra’s algorithm.
| Graph theory (5): Binary trees, Huffman’s algorithm. Greedy algorithms. Property of matroid.
| Graph theory (6): Matchings. Bipartite graphs. Matchings in bipartite graphs. Maximum matching and complete matching: Hall’s and Berge’s theorems.
| Graph theory (7): Transportation networks. Flows and cuts. Max flow min cut theorem.
